i am pretty sure your buttonhole would be lost in the felting process, but it is completely safe to cut a fabric once it is felted. i wound up not using pockets i had felted to attach to a bag and cut them into fabulous little coasters.
your stitches will be mostly lost, yes. if you don’t want them lost, you can felt the completed item less, but if you’re going to be cutting it, make sure it is felted enough to allow for the cutting. My first felted creation, I could’ve probably felted it a bit more and you can kinda sorta see the V’s and some rows on the RS, but barely. Here is a good close-up of the Booga Bag from Black Sheep and you can see in that picture what I mean.
good luck and have fun!!!